Correction of errors in estimates of T₁ at low spin-lock amplitudes in the presence of B₀ and B₁ inhomogeneities

Relaxation rates R-1 rho in the rotating frame measured by spin-lock methods at very low locking amplitudes (<= 100 Hz) are sensitive to the effects of water diffusion in intrinsic gradients and may provide information on tissue microvasculature, but accurate estimates are challenging in the presence of B-0 and B-1 inhomogeneities. Although composite pulse preparations have been developed to compensate for non-uniform fields, the transverse magnetization comprises different components and the spin-lock signals measured do not decay exponentially as a function of locking interval at low locking amplitudes. For example, during a typical preparation sequence, some of the magnetization in the transverse plane is nutated to the Z-axis and later tipped back, and so does not experience R-1 rho relaxation. As a result, if the spin-lock signals are fit to a monoexponential decay with locking interval, there are residual errors in quantitative estimates of relaxation rates R-1 rho and their dispersion with weak locking fields. We developed an approximate theoretical analysis to model the behaviors of the different components of the magnetization, which provides a means to correct these errors. The performance of this correction approach was evaluated both through numerical simulations and on human brain images at 3 T, and compared with a previous correction method using matrix multiplication. Our correction approach has better performance than the previous method at low locking amplitudes. Through careful shimming, the correction approach can be applied in studies using low spin-lock amplitudes to assess the contribution of diffusion to R-1 rho dispersion and to derive estimates of microvascular sizes and spacings. The results of imaging eight healthy subjects suggest that R-1 rho dispersion in human brain at low locking fields arises from diffusion among inhomogeneities that generate intrinsic gradients on a scale of capillaries (similar to 7.4 +/- 0.5 mu m).